Exact Set Cover

GPTKB entity

Statements (28)
Predicate Object
gptkbp:instanceOf theoretical computer science
gptkbp:alsoKnownAs gptkb:Exact_Cover
gptkbp:application Polyomino packing
Sudoku solving
Tiling problems
gptkbp:category gptkb:Theoretical_computer_science
mathematical optimization
gptkbp:complexity NP-complete
gptkbp:decision Does there exist a subcollection of subsets that covers each element exactly once?
gptkbp:definedIn Given a universe and a collection of subsets, find a subcollection that partitions the universe
gptkbp:firstDescribed gptkb:Donald_Knuth
1970s
gptkbp:hasVariant gptkb:Exact_Cover_by_3-Sets_(X3C)
https://www.w3.org/2000/01/rdf-schema#label Exact Set Cover
gptkbp:input collection of subsets
universe of elements
gptkbp:output subcollection of subsets
gptkbp:outputCondition each element is covered exactly once
gptkbp:reduces gptkb:3-SAT
gptkb:Exact_Cover_by_3-Sets_(X3C)
gptkb:Sudoku
gptkbp:relatedTo gptkb:Set_Cover_Problem
NP-complete problem
gptkbp:solvedBy gptkb:Algorithm_X
gptkb:Dancing_Links
gptkbp:bfsParent gptkb:Karp's_21_NP-complete_problems
gptkb:Reducibility_Among_Combinatorial_Problems_(Karp,_1972)
gptkbp:bfsLayer 6